laser scanning systems

ABSTRACT

The invention provides a method of reducing jitter error in a laser scanning system ( 1 ) adapted to produce a scanned image comprising a number of lines of an object ( 18 ). The method comprising the steps of providing a reference object ( 22 ) arranged such that the scanned image produced by the laser scanning system ( 1 ) includes a reference image ( 24 ) of the reference object ( 22 ); processing the reference image ( 24 ) to calculate an error arising from non-repeatable displacement of the lines of the reference image ( 24 ); and adjusting at least one operating parameter of the laser scanning system ( 1 ) in response to the calculated error.

The present invention relates to laser scanning systems, especially, butnot exclusively, to laser scanning systems utilised in scanning laserophthalmoscopes.

Laser scanning systems, such as those found in scanning laserophthalmoscopes, typically comprise of a high speed rotating polygonalmirror and a motor driven slow speed mirror which are used to create araster scan pattern of, for example, a human retina. The polygon mirrorhas a plurality of facets and provides the vertical scanning of thelaser beam, and the slow speed mirror provides the horizontal scanningof the laser beam. Each facet of the polygon mirror generates onevertical scan line of image per polygon rotation.

The resolution of the images produced by such systems relies on anaccurate timing of the polygon facet arrival in position which triggersthe recording of a scan line.

A conventional approach to ensuring an accurate timing of the polygonfacet arrival involves the use of a facet detector. The facet detectoruses a laser beam that impacts on the polygon facet from a side angleand detects when the orientation of the facet is normal to the plane ofthe detector. When the polygon facet is in position an electronic systemtriggers a clock signal for the recording of a scan line. The timingsignal of facet arrival is therefore used for accurate line scanregistration.

However, the facet detector and the polygon both introduce some “jitter”error to the scanned image. Jitter is the non-repeatable displacement ofa line along the scan direction. The effect of this jitter error is tointroduce vertical shifts between vertical lines of the scanned image,which affects the quality of the image produced.

Jitter error can be either random or periodic in nature. Jitter errormay result from:

-   -   (a) Imperfect timing of the polygon facet position. If the clock        signal is started when the polygon facet is not exactly normal        to the plane of the detector, the entire vertical line of the        image will be shifted in the vertical direction.    -   (b) Random noise introduced by the electronic triggering system        of the facet detector. If the triggering of the clock signal for        the recording of a scan line is early, or late, the entire        vertical line of the image will be shifted in the vertical        direction.    -   (c) Variations of the cut depth in the facets of the polygon.        Facet cut depth error is the deviation from facet to facet of        the distance from the centre of the facet to the centre of the        axis of rotation. The effect of these variations is to cause        periodic vertical shifts in the scan line.    -   (d) Variations in the flatness of the facet of the polygon.        Variations in flatness from facet to facet will result in        periodic jitter in the scan line.    -   (e) Variations in the rotational speed of the polygon. The        rotational speed of the polygon can be affected by noise from        the mounting bearings. The effect of these variations in        rotational speed of the polygon is to cause random vertical        shifts in the scan line.

It is an object of the present invention to provide improved techniquesfor removing jitter error in laser scanning systems.

According to a first aspect of the present invention there is provided amethod of reducing jitter error in a laser scanning system adapted toproduce a scanned image comprising a number of lines of an object, themethod comprising the steps of:

-   -   providing a reference object arranged such that the scanned        image produced by the laser scanning system includes a reference        image of the reference object;    -   processing the reference image to calculate an error arising        from non-repeatable displacement of the lines of the reference        image; and    -   adjusting at least one operating parameter of the laser scanning        system in response to the calculated error.

Adjusting the at least one parameter of the laser scanning system inresponse to the calculated error exploits the linear dependency betweenthe error arising from the non-repeatable displacement of the lines ofthe reference image and line shifts in the reference image. This allowsthe line shifts to be incorporated as operating parameter controlvariables in the laser scanning system to reduce the jitter error whencapturing an image.

The reference object may be periodic in the direction of the line ofscan of the laser scanning system. The line of scan is the line in whichthe scanning laser beam moves across the reference object as it producesa line of the scanned image.

The reference object may include a series of alternate black and whitebands. The alternate black and white bands may be equally spaced. Thewidth of each band may be between 0.25 mm and 0.75 mm. Preferably, thewidth of each band is 0.5 mm. The reference image thus contains aplurality of columns of alternate black and white sections.

The reference image may comprise a number of pixels.

The laser scanning system may further comprise a source of collimatedlight.

The laser scanning system may comprise first and second scanningelements. The first scanning element may be a rotating polygonal mirror.The second scanning element may be an oscillating plane mirror.

The reference object may be positioned in the optical path of the laserscanning system after the first scanning element. That is, the referenceobject may be positioned in the optical path of the laser scanningsystem between the first scanning element and the second scanningelement.

When the first scanning element is a rotating polygonal mirror and thereference object is positioned after the polygon in the optical path,the scanning laser beam repeatedly moves across the same portion of thereference object to produce the reference image. That is, the referenceimage is constructed of a plurality of repeat image scans of the sameportion of the reference object. The scanned image produced by the laserscanning system in this case includes only this reference image.

The source of collimated light and the first and second scanningelements may combine to provide a two-dimensional collimated light scan.

The second scanning element may be positioned in the optical path of thelaser scanning system after the first scanning element and the referenceobject may be positioned after the second scanning element such that thesource of collimated light and the first and second scanning elementscombine to produce a two-dimensional raster scan light pattern acrossthe reference object to produce the reference image thereof.

The laser scanning system may further comprise scan transfer meanshaving two foci.

The source of collimated light and the first and second scanningelements may combine to provide a two-dimensional collimated light scanfrom an apparent point source, and the apparent point source may beprovided at a first focus of the scan transfer means and an object maybe accommodated at a second focus of the scan transfer means, andwherein the scan transfer means may transfer the two-dimensionalcollimated light scan from the apparent point source to the object.

The object may be an eye and the scan transfer means transfers thetwo-dimensional collimated light scan from the apparent point sourceinto the eye.

The scan transfer means may comprise an elliptical mirror. The scantransfer means may comprise an aspherical mirror. The scan transfermeans may comprise an ellipsoidal mirror. The scan transfer means maycomprise a pair of parabola mirrors. The scan transfer means maycomprise a pair of paraboloidal mirrors.

The laser scanning system may further comprise scan relay means. Thesource of collimated light, the first and second scanning elements andthe scan relay means may combine to provide the two-dimensionalcollimated light scan from the apparent point source.

The scan relay means may comprise two foci. One foci of the scan relaymeans may be coincident with one foci of the scan transfer means.

The scan relay means may comprise an elliptical mirror. The scan relaymeans may comprise an aspherical mirror. The scan relay means maycomprise an ellipsoidal mirror. The scan relay means may comprise a pairof parabola mirrors. The scan relay means may comprise a pair ofparaboloidal mirrors.

The reference object may be located on one of the scan transfer means orscan relay means.

The scanned image produced by the laser scanning system may include animage of the object and the reference image of the reference object.

The image of the object and the reference image of the reference objectmay occur beside one another on the scanned image.

The reference image may extend along an edge portion of the scannedimage.

The step of processing the reference image may include assigning onecolumn of the reference image as the reference column. Preferably, thereference column is located around the centre of the reference image.

The step of processing the reference image may include generating datasignals for one or more columns which are representative of the imageinformation of the column. The image information of the column mayinclude the light intensity, or brightness, of the image and the datasignals may include values which are representative of this intensity,or brightness. The light intensity, or brightness, may include the lightintensity or brightness of each pixel in the reference image.Preferably, data signals are generated for each column of the referenceimage.

The step of processing the reference image may further include comparingthe reference column data signal with one or more data signals from theother columns. Preferably, the reference column data signal is comparedwith every other column data signal.

The comparison between the reference column data signal and the othercolumn data signals may further include determining the similaritiesbetween the signals. Preferably, the comparison between the referencecolumn data signal and the other column data signals includesdetermining the warping between the signals.

The comparison between the reference column data signal and the othercolumn data signals may include using a dynamic time warping algorithm.The comparison between the reference column data signal and the othercolumn data signals may include using a derivative dynamic time warpingalgorithm.

The comparison between the reference column data signal and the othercolumn data signal may include generating a matrix which isrepresentative of the pair-wise distances between the reference columndata signal and the other column data signal. A matrix is generated foreach comparison of the reference column data signal with every othercolumn data signal. The distances between each column may be defined interms of pixels. That is, the distance between corresponding points ofeach signal may be represented by an integer number of pixels.

The comparison between the reference column data signal and the othercolumn data signal may alternatively include generating a matrix whichis representative of the pair-wise distances between the derivative ofthe reference column data signal and the derivative of the other columndata signal. A matrix is generated for each comparison of the referencecolumn data signal with every other column data signal. Preferably, thederivative is the pair-wise distances between the first derivative ofthe reference column data signal and the derivative of each of the othercolumn data signals.

The comparison between the reference column data signal and the othercolumn data signals further includes determining a functionrepresentative of the minimal distance path of the matrix. The minimaldistance path may be termed the “alignment path”, the “optimal path”,the “minimal cost path”, the “warping path”, or the “warping function”.

The determination of the function representative of the minimal distancepath of the matrix may include applying one or more constraints. Theconstraints may include that the function satisfies a boundary conditioncriteria, where the starting and end points of the function must be thefirst and last points of the sequence. That is, this requires thefunction to start and finish in diagonally opposite corners of thematrix. The constraints may further include that the function satisfiesthe monotonicity criteria. That is, this requires the function to bemonotonically spaced in time (i.e. the function must be increasing intime). The constraints may further include that the function satisfiesthe continuity criteria. This restricts the allowable steps in thewarping path to adjacent cells. That is, the function can only progressin steps of one at a time.

The step of processing the reference image may further includedetermining an approximate signal shift between the reference columndata signal and each of the other column data signals. The signal shiftmay correspond to a column shift in the reference image. The columnshift corresponds to the error arising from the quasi-periodicdisplacement of the columns of the reference image.

The determination of the approximate signal shift between the referencecolumn data signal and the other column data signals may includetransforming a parametric representation of the function to an explicitform.

The transformation may include removing duplicates of the abscissas ofthe parametric curve.

The transformation may include interpolation of the explicit form of thefunction.

The determination of the approximate signal shift between the referencecolumn data signal and each of the other column data signals may includedetermining the distance between the interpolated path defined by theexplicit function and a reference path in the matrix.

The reference path in the matrix corresponds to the matrix diagonal.

The parametric representation of the matrix diagonal is X=t. Y=t, t in[1,N], where N is the signal length. The implicit form is Y=X. Theimplicit form corresponds to the path between the two signals if theywere identical.

The step of processing the reference image may include determining anaverage approximate signal shift for all column data signals originatingfrom the same portion of the scanning element of the laser scanningsystem.

The step of processing the reference image may include determining anaverage approximate signal shift for all column data signals originatingfrom the same facet of the rotating polygonal mirror.

The step of adjusting the at least one operating parameter of the laserscanning system in response to the calculated error may includeadjusting the capture time of the first or second scanning elements.

The capture time is the time taken to record a scan line across thescanning element.

The capture time of the first or second scanning element may be advancedand/or delayed.

Where the first or second scanning element is a rotating polygonalmirror, each facet of the polygon may have a specific capture time.

The capture time for each facet of the polygon may be determined byadvancing or delaying a reference capture time by a factor dependentupon the average approximate signal shift for that specific portion ofthe scanning element. The specific portion of the scanning element maybe a facet of the polygon.

According to a second aspect of the present invention there is provideda mirror for a laser scanning system including a reference object.

The reference object may be periodic in the direction of the line ofscan of the laser scanning system. The reference object may be made upof a series of alternate black and white bands.

The mirror may be an elliptical mirror, an aspherical mirror, anellipsoidal mirror, a parabola mirror or a paraboloidal mirror.

Embodiments of the present invention will now be described, by way ofexample only, with reference to the accompanying drawings, in which:

FIG. 1 is a schematic view of the scanning and reflecting elements of alaser scanning ophthalmoscope;

FIG. 2 is a first partial schematic view of the elements of FIG. 1;

FIG. 3 is a second partial schematic view of the elements of FIG. 1;

FIG. 4 is a flow chart detailing the method of reducing jitter error inthe laser scanning system in accordance with the present invention;

FIG. 5 is an example of a scanned image produced by the laser scanningsystem of FIG. 1;

FIG. 6 a is a graph illustrating two column data signals from thereference image of FIG. 5;

FIG. 6 b is a graph illustrating the two column signals of FIG. 6 aafter an approximate shift has been applied to the second signal;

FIG. 7 is a pair-wise distance matrix between a reference column and asecond column of the reference image;

FIG. 8 is a schematic representation of the approximated column shifterror in the reference image;

FIG. 9 is an example of a corrected scanned image produced by the laserscanning system of FIG. 1; and

FIG. 10 is a schematic view of an alternative embodiment of thereflecting and scanning elements of the laser scanning ophthalmoscope ofFIG. 1.

FIG. 1 is a schematic view of the scanning and reflecting elements ofthe laser scanning system 1, as applied to a scanning laserophthalmoscope (SLO). As illustrated, the main components are a highspeed rotating polygon mirror 10 (an example of a first scanningelement), a slow speed mirror 12 (an example of a second scanningelement), a first ellipsoidal mirror (slit mirror) 14 (an example ofscan relay means) and a second ellipsoidal mirror (main mirror) 16 (anexample of a scan transfer means).

The slow speed mirror 12 may be an oscillating plane mirror, such as agalvanometer mirror.

The rotating polygon mirror 10 is located at the first focal point ofthe slit mirror 14 and the slow speed mirror 12 is located at the secondfocal point of the slit mirror 14. The slow speed mirror 12 is alsolocated at the first focal point of the main mirror 16. A patient's eye18 is located at the second focal point of the main mirror 16.

A source of collimated light 20 a produces a laser light beam 20. Thelaser light beam 20 is then reflected from the polygon 10 to thepatient's eye 18 via the slit mirror 14, the slow speed mirror 12 andthe main mirror 16.

The slit mirror 14 acts as an optical amplifier, as it amplifies thescanning aperture of the beam 20. For example, with reference to FIG. 2,if the polygon 10 has 16 facets, it will rotate 22.5 degrees betweenfacets and the resulting scanning aperture α of the beam 20 on the slitmirror 14 will be 45 degrees. After the beam 20 is scanned across theslit mirror 14, the scanning aperture β is 120 degrees.

With reference to FIG. 3, the beam 20 is then scanned across the mainmirror 16 by the slow speed mirror 12 and reflected into the patient'seye 18. The source of collimated light 20 a, the polygon 10 and the slowspeed mirror 12 combine to provide a two-dimensional collimated lightscan. The laser scanning system 1 therefore produces a scanned imagecomprising a number of lines of an object, e.g. a human retina.

The source of collimated light 20 a, the polygon 10 and the slow speedmirror 12 may also combine to provide a two-dimensional collimated lightscan from an apparent point source, and the apparent point source may beprovided at the first focus point of the main mirror 16, such that themain mirror 16 transfers the two-dimensional collimated light scan fromthe apparent point source into the patient's eye 18.

The main mirror 16 may comprise an elliptical mirror, an asphericalmirror, an ellipsoidal mirror, a pair of parabola mirrors or a pair ofparaboloidal mirrors.

The slit mirror 14 may comprise an elliptical mirror, an asphericalmirror, an ellipsoidal mirror, a pair of parabola mirrors or a pair ofparaboloidal mirrors.

This type of laser scanning ophthalmoscope is described in theApplicant's European Patent Nos. 0730428 and 07733214.6.

FIG. 1 also illustrates a reference object 22. In the embodimentdescribed and illustrated here the reference object 22 is a stripedtarget comprising a series of alternate black and white bands. The bandsare equally spaced with the width of each band being betweenapproximately 0.25 mm and 0.75 mm. Ideally the width of each band isapproximately 0.5 mm.

The reference object 22 is placed in the laser scanning system 1 beforethe system is used to obtain an image of the patient's retina.

The reference image is positioned between the polygon 10 and the slitmirror 14 such that is in the line of scan of the laser scanning system1, i.e. the laser beam 20 moves across the reference object 22 duringoperation of the laser scanning system 1. The reference object 22 istherefore periodic in the direction of the line of scan of the laserscanning system 1.

With the reference object 22 positioned in the optical path after thepolygon 10, i.e. between the polygon 10 and the slow speed mirror 12,the laser beam 20 repeatedly moves across the same portion of thereference object 22 to produce the reference image 24 (see FIG. 5below). That is, the reference image 24 is constructed of a plurality ofrepeat image scans of the same portion of the reference object 22.

As illustrated in FIG. 5, the reference image 24 comprises a pluralityof columns 25 of alternate black and white bands. The reference image 24may comprise a number of pixels. Each column (scan line) 25 contains ajitter error that manifests itself as a vertical shift. That is, eachcolumn 25 of the reference image 24 contains a displacement along thescan direction of the polygon 10. This displacement is quasi-identicalin columns occurring from the same polygon facet. That is, thedisplacement values are quasi-periodic. Small differences of less than ¼pixel may result from noise in the system which prevents thedisplacements occurring from the same polygon facet from being exactlyidentical.

Typically, the reference image 24 comprises 3900 columns (and 3072lines). However, it should be appreciated that the scanned referenceimage 24 may comprise any suitable number of columns 25.

The method for reducing the jitter error in the laser scanning system 1will now be described with reference to FIGS. 4 to 8.

With reference to FIG. 4, in step 1 the reference image 24 is capturedby the laser scanning system 1. As described above, the laser beam 20repeatedly moves across the striped target of the reference object 22 toproduce the reference image 24 of FIG. 5. In obtaining the referenceimage 24 the laser scanning system 1 uses the green channel (i.e.wavelength of approximately 510 nm).

The reference image 24 may be a pixelated image with m rows of n columns(i.e. m×n). (For example, m=3072, n=3900).

Steps 2 to 6 describe how the reference image 24 is processed tocalculate the error arising from non-repeatable displacement of thecolumns 25 of the reference image 24.

In step 2 a reference column 26 from the columns 25 of the referenceimage 24 is determined. The reference column 26 is determined using theformula n/2, where n is the total number of columns 25.

In step 3 the similarity between the reference column 26 and each of theother columns 25 is determined. The similarity between the referencecolumn 26 and each of the other columns 25 is determined by using adynamic time warping (DTW) algorithm or a derivative dynamic timewarping (DDTW) algorithm. DTW and DDTW are known techniques forefficiently finding an alignment between two signals (or sequences).DDTW and DTW compare vectors locally, looking at local trends and/orvariations between vectors.

In the embodiment described and illustrated here a DDTW algorithm isused to find alignment between the reference column signal and everyother column signal. However, it should be appreciated that DTW mayalternatively be used.

The warping between the reference column 26 and each of the othercolumns 25 is determined by firstly generating data signals (vectorsequences) for each column 25 (including the reference column 26) whichare representative of the image information of the column. The imageinformation of the column may include the light intensity, orbrightness, of the image and the data signals may include values whichare representative of this intensity, or brightness. Where the referenceimage 24 is a pixelated image, the light intensity, or brightness, mayinclude the light intensity or brightness of each pixel in the referenceimage.

The data signals may be represented as vectors:

R=r₁, r₂, . . . , r_(i), . . . , r_(n),

C=c₁, c₂, . . . , c_(j), . . . , c_(m),

-   -   where R is the reference column signal        -   C is one of the other column signals        -   n and m are the lengths of the signals.        -   (In the present embodiment m=n, as all columns have the same            length=3072.)

The data signals are illustrated in FIG. 6 a. As illustrated in FIG. 6a, the two signals R and C are out of alignment with one another. Asexplained above, this is a result of the jitter error.

To find the alignment between the two signals using DDTW an n by mmatrix is constructed where the (i^(th),j^(th)) element of the matrixcontains the pair-wise distance d(r_(i),c_(j)) between the two pointsr_(i) and c_(j). Using DDTW the distance d(r_(i),c_(j)) is not Euclideanbut rather the square of the difference of the estimated derivatives ofr_(i) and c_(j). The distance matrix is therefore:

D[i,j]((r _(i))′−(c _(j))′)((r _(i))′−(c _(j))′) with 1≦i≦m and 1≦j≦m,

-   -   where (r_(i))′, (r_(j))′, and (c_(j))′ are the derivatives of R        and C at points i and j.

Each matrix element (i,j) corresponds to the alignment between thepoints r_(i) and c_(j). The distance matrix D[i,j] between the datasignals {umlaut over (R)} and {umlaut over (C)} is illustrated in FIG.7.

Once the matrix is constructed, the DDTW algorithm finds the alignmentpath which runs through the “low cost” areas, or “valleys”, on thematrix. This alignment path is an example of a function representativeof the minimal distance path of the matrix. The minimal distance pathmay be termed the “alignment path”, the “optimal path”, the “minimalcost path”, the “warping path”, or the “warping function”.

The alignment path is a contiguous (in the sense stated below) set ofmatrix column and row indexes (or coordinates) that defines a mappingbetween R and C.

The alignment path constructed by the DDTW algorithm may be expressedas:

P=(p ₁ , p ₂ , . . . , p _(k) , . . . , p _(K)) with max(m, n)≦K<m+n−1,

-   -   where the k^(th) element of P is defined as p_(k)=(px,py)_(k).

The alignment path P is subject to certain constraints:

-   -   (a) Boundary conditions: p₁=(1,1) and p_(K)=(m,n). This requires        the alignment path to start and finish in diagonally opposite        corner cells of the matrix, i.e. the starting and end points of        the alignment path must be the first and last points of the        sequences.    -   (b) Monotonicity: Given p_(k)=(a,b), then p_(k−1)=(a′,b′) where        a−a′≧0 and b−b′≧0. This forces the points in the alignment path        P to be monotonically spaced in time, i.e. the coordinates of        the alignment path must be increasing.    -   (c) Continuity: Given p_(k)=(a,b), then p_(k−1)=(a′,b′) where        a−a′≦1 and b−b′≦1. This restricts the allowable steps in the        alignment path P to adjacent cells (including diagonally        adjacent cells), i.e. the path can only go one step up, or left,        or both.

There may be many alignment paths which satisfy the above criteria.However, it is necessary to determine the path which minimizes thewarping cost, i.e. the optimal path.

The optimal alignment path should minimize the warping cost:

${{{DDTW}\left( {R,C} \right)} = {\min\left( \frac{\sqrt{{\sum\limits_{k = 1}^{K}p_{k}}\;}}{K} \right)}},$

-   -   where K in the denominator is used to compensate for the fact        that the alignment paths may have different lengths.

The alignment path can be found by evaluating the following recurrencewhich defines the cumulative distance γ(i,j) as the distance d(i,j)found in the current cell and the minimum of the cumulative distances ofthe adjacent elements:

γ(i,j)=d(r _(i) ,c _(i))+min{γ(i−1,j),γ(i,j−1)}.

The alignment path is illustrated in FIG. 7, referenced as 28. FIG. 7also illustrates the reference column and other column data signals Rand C.

The pseudo code for determining the matrix and the alignment path aredetailed in Annexes 1 and 2.

FIG. 6 b illustrates the mapping of signal C onto signal R. Asillustrated, once the alignment path is known it can be used to producea close mapping of signals.

In step 4 the warping between the reference column data signals and theother column signals is approximated with a shift (or offset). The shiftbetween signals corresponds to a column shift in the reference image 24.The column shift corresponds to the error arising from thenon-repeatable displacement of the columns 25 of the reference image 24.

The alignment path has the form:

P=(p _(i) , p ₂ , . . . , p _(K))

-   -   with p_(k)=(p_(k)x,p_(k)y) are the coordinates of each point in        the path.

This is therefore the parametric representation of the curve of thealignment path.

The parametric representation is then transformed to an explicit form:

p _(k) y=f(p _(k) x) with 1≦k≦K.

The transformation is obtained by removing duplicates of the abscissasof p, obtaining their corresponding coordinates and then interpolatingthe results over the frame [1,m]. In the embodiment described here, m=nis the length of the two original signals R and C.

The pseudo code for removing the abscissas of p and interpolating theresults over the frame [1,m] are detailed in Annexes 3 and 4.

The shift is obtained by comparing the implicit form of the alignmentpath with the diagonal reference path of the matrix.

The reference path of the matrix has a parametric representation X=t,Y=t, t in [1,N] where N is the signal length. The implicit form of thereference path is Y=X. The reference path would be the same as thealignment path if the two compared signals were identical. That is, theshift is obtained by comparing the discrete form of the alignment pathwith an “ideal path”, i.e. the path that would exist if there were nowarping between the two data signals.

The alignment path 28 and the reference path 30 are illustrated in FIG.7.

The pseudo code for comparing the discrete form of the alignment pathwith the diagonal distance path of the matrix and obtaining the shiftbetween each signal is detailed in Annex 5. The shift signal may bereferenced as s (see FIG. 4).

It should be noted that the above-described shift is determined betweenthe reference column 26 and every other column 25. The result of this isthat n shift values for each column 25 (n=3900).

In step 5 the column shift for each facet of the polygon 10 isdetermined. Given that most of the jitter present in the reference image24 is polygon facet dependent, the average of all the shifts of thecolumns 25 originating from the same polygon facet is averaged. In thecase where the polygon 10 has 16 facets, these columns (or pixels) areseparated by 16 columns (or pixels).

The column shift for each facet of the polygon 10 may be determined by:

${{{Offset}(j)} = {\sum\limits_{k,{{n - 16 + j} \geq 1}}^{k,{{n - {16k} + j} \leq n}}\underset{\_}{\underset{\_}{s}\left\lbrack {\left( {n - {16k}} \right) + j} \right\rbrack}}},$

-   -   where Offset(j) is the column shift for each facet and        -   k k is an index representing image columns        -   n number of columns in the image (n=3900)        -   j variable corresponding to each facet. Here 1≦j≦16

The approximated column shift error in the reference image 24 isillustrated in FIG. 8. Columns which originate from the same facet ofthe polygon 10 are referenced with the number 32. The reference column26 is also illustrated.

FIG. 8 thus illustrates the averaged calculated error arising fromnon-repeatable displacement of the columns of the reference image 24.From FIG. 8 it can clearly be seen that the same column shift value hasbeen assigned to each column 25 originating from the same facet of thepolygon 10.

In step 6 the column shift (or offset) determined in step 5 isapproximated to 0.25 pixel accuracy. This is due to the fact that thesampling of the scan has 0.25 pixel rate.

The approximated offset can be calculated by:

Offset(j)=0.25×(round(Offset(j))).

Thus, for example, if the offset value was calculated as having a valueof 1.6, it would be approximated to 0.25 pixel accuracy to 1.5.

In step 7 a scanning time delay (capture time) of the polygon 10 of thelaser scanning system 1 is determined based on the approximated offsetvalue determined in step 6. This scanning time delay of the polygon ofthe laser scanning system 1 is an example of an operating parameter ofthe laser scanning system 1.

In the embodiment described and illustrated here, each pixel of thereference image 24 is scanned at a frequency of 132 MHz, i.e. 7.57 ns.

This yields a linear relationship between the time delay and the offsetof step 6 as:

Time Delay(ns)=7.57×Offset(j).

This time delay is applied to each facet of the polygon 10 of the laserscanning system 1. That is, the time delay, or capture time, for eachfacet of the polygon is determined by advancing or delaying a referencecapture time by a factor dependent upon the average approximate signalshift for that specific facet of the polygon.

The system may start imaging with the longest facet of the polygon 10.In order to know which shift corresponds to which facet of the polygon10, the system 1 is forced to always start scanning using the longestfacet. The facet data are recorded during an initial stage which imagingis started with facet 1, for example. The DDTW algorithm is run duringthis stage to obtain 16 shift values. s1 corresponding to facet 1, s2corresponding to facet 2 etc. If a second image is captured, there is noway of knowing if the imaging will start with facet 1, and therefore noguarantee that the offsets will be applied correctly. To overcome this,imaging is started with the longest facet, as determined by the initialstage. Since the polygon always rotates in the same direction, andknowing the longest facet (or reference facet) and its offset, it ispossible to attribute the remaining offsets correctly.

Once the time delay values (operating parameters) of the polygon 10 ofthe laser scanning system 1 have been adjusted in response to thecalculated errors, the reference object 22 is scanned again. An exampleof the reduced jitter error reference object image 24′ is illustrated inFIG. 9. It can clearly be seen that the jitter error has been reducedmarkedly from the original reference image 24 of FIG. 5.

Once the start of scan time delay/advance values of the polygon 10 ofthe laser scanning system 1 have been adjusted in response to thecalculated errors, the reference object 22 is removed from the systemand the system is used to obtain an image of the patient's retina in thenormal manner. With this adjustment, the image of the patient's retinahas a greatly reduced jitter error.

Steps 1 to 7 are preferably carried out by a computer, processing means,or the like. The steps 1 to 7 may be incorporated as part of theexisting computer control software of the laser scanning system 1. Thesteps 1 to 7 may be provided on a separate computer, or the like, fromthe existing computer of the laser scanning system 1.

Step 7 is carried out by a computer, processing means, or the like,which is used to control the scanning elements 10, 12 of the laserscanning system 1. The software of the computer of the laser scanningsystem 1 controls the start of scan time 12. The software isreprogrammed to adjust the operating parameters of the laser scanningsystem 1 in response to the calculated error to correct for thenon-repeatable displacement of the lines of the reference image 24.

FIG. 10 is an alternative embodiment of the laser scanning system 1. Thesecond embodiment is similar to the first embodiment, with the exceptionthat the reference object 22′ is located on the slit mirror 14.

The reference object 22′ is placed on the edge of the slit mirror 14.Therefore, the scan laser beam 20 moves across the reference object 22′and the slit mirror 14 during operation of the laser scanning system 1′.

This means that the scanned image produced by the laser scanning system1′ includes an image of the patient's eye 18 and a reference image ofthe reference object 22′. That is, the scanned image is a twodimensional image which includes a portion of the patient's eye 18 and aportion of the reference object 22′.

In the embodiment described and illustrated here the reference object22′ covers approximately 2.5% of the scanning aperture and is imaged atthe beginning of every scan line.

The method of reducing the jitter error in the laser scanning system 1′is the same as that described above in respect of the first embodimentof the laser scanning system 1.

The method of the present invention therefore obviates or mitigates thedisadvantages of previous proposals by correcting for the jitter errorintroduced to the scanned image from the imperfect timing of the polygonfacet position, the random noise introduced by the triggering system ofthe facet detector, the variations in the cut-depth of the facets of thepolygon, the variations in the flatness of the facet of the polygon andthe variations in the rotational speed of the polygon. The benefits ofthe method are increased jitter measurement accuracy, improved visualappearance of the scanned image, reduced facet detector accuracyrequirements, reduced polygon building requirements, reduced polygon andfacet detector failures in the field and improved polygon performancemonitoring.

The method of the present invention exploits the linear dependencybetween imaging signal delay and pixel shifts and incorporates theshifts as timing delays when capturing the image. The method does notrequire any image processing, which reduces the computational cost.Since the method may be performed as a calibration before imaging of thepatient's eye, the time taken to obtain the image of the patient's eyeis unchanged, as the shift errors have already been corrected forbeforehand.

Modifications and improvements can be made to the above withoutdeparting from the scope of the present invention. For example, althoughthe laser scanning systems 1, 1′ have been illustrated above ascomprising slit mirrors 14, it is not essential that the system includesa slit mirror. In this case the reference object 22 is placed in theoptical path after the polygon 10 or located on the main mirror 16.

Furthermore, it is also possible that the reference object 22 ispositioned in the optical path after the slow speed mirror 12 and thepolygon 10, i.e. the reference object 22 may be positioned in the systemsuch that the polygon 10 and the slow speed mirror 12 combine to producea two-dimensional raster scan light pattern across the reference object22 to produce the reference image.

Also, the step of generating data signals for each column 25 may notnecessarily include all columns in the reference image 24. It ispossible to only generate data signals for a portion of these columns,i.e. a portion of the reference image.

Furthermore, although the method of reducing the jitter error in a laserscanning system has been described above with respect to the rotatingpolygon scanning element, it should be appreciated that the method couldbe applied to correcting for non-repeatable line displacement errors inthe reference image caused by other scanning elements, e.g. oscillatingplane mirrors (slow speed mirrors), or any other rotating and/oroscillating reflective elements used in the scanning system.

Annex 1 Accumulated Cost Matrix(X;Y;D) //X and Y are input signals, D isthe distance matrix defined as piece- //wise squared distances between Xand Y in the case of DTW, or //piece- wise distances between the firstderivatives of X and Y in the //case of DDTW--------------------------------------------------------------------------------------------------- 1: m ←[X] //m is the size of X  2: m ←[Y] //m is the size of Y. In ourcase X and Y have the same length  3: ddtw[ ] ← new [m ,m] //allocatespace for ddtw:the Accumulated Cost Matrix  4: ddtw(0,0) ← 0//initialize temporary variable  5: for i = 1; i ≦ m; i ++, do  6:ddtw(i; 1) ← ddtw(i−1; 1) + D(i; 1) //fill first column of ddtw  7: endfor  8: for j = 1; j ≦ m; j ++, do  9: ddtw(1; j) ← ddtw(1; j−1) + D(1;j) //fill first column of ddtw 10: end for 11: for i = 1; i ≦ m; i ++,do 12: for j = 1; j ≦ m; j ++, do 13: ddtw(i; j) ← D(i; j)+min {ddtw(i −1; j); ddtw(i; j − 1); ddtw(i − 1; j − 1)}//fill rest of matrix 14: endfor 15: end for 16: return ddtw //return accumulated cost matrix ddtw---------------------------------------------------------------------------------------------------

Annex 2 Optimal Warping Path(ddtw)--------------------------------------------------------------------------------------------------- 1: path[ ] ← new array //allocate space for the warping path  2: i =rows(ddtw) //i is an index for ddtw rows  3: j = columns(ddtw) //j isindex for ddtw columns //The following steps fill the path by abacktracking algorithm from point (m,m) to point (1,1)  4: while (i > 1)& (j > 1) do  5: if i == 1 then  6: j = j − 1  7: else if j == 1 then 8: i = i − 1  9: else 10:  if ddtw(i−1; j) == min {ddtw(i − 1; j);ddtw(i; j − 1); ddtw(i − 1; j − 1)} 11:  then 12: i = i − 1 13: else ifddtw(i; j−1) == min {ddtw(i − 1; j); ddtw(i; j − 1); ddtw(i − 1; j − 1)}14: then 15: j = j − 1 16:  else 17: i = i − 1; j = j − 1 18:  end if19: path:add((i; j)) 20: end if 21: end while 22: return path---------------------------------------------------------------------------------------------------

Annex 3 Remove Abscissa Duplicates(path) //the path obtained from theAnnex 2 is in the form (xk,yk) 1≦k≦K, //we need to write this path inthe form Yk=f(Xk) 1≦k≦K. To be able to do so. we need remove duplicatesfrom xk 1≦k≦K.--------------------------------------------------------------------------------------------------- 1: new_path[ ] ← new array  2: K = length(pathx) //K is the length ofthe x-coordinates (abscissas) of the path  3: new_pathx(1)=pathx(1)  4:j=1 //initialize index of elements of newpath  5: for i = 1; i ≦ K−1; i++, do  6: if pathx(i+1)!=pathx(i)  7: new_pathx(j+1)=pathx(i+1)  8:new_pathy(j+1)=pathy(i+1)  9: j=j+1 10: end if 11: end for---------------------------------------------------------------------------------------------------

Annex 4 Interpolate New Path(x[1...m],xi[1..Ni], yi[1..Ni],)) //theprevious step Annex3 gave a modified path without repetition. // The newpath doesn't necessarily cover all the range [1,m] where m is the sizeof the input signals. We therefore interpolate the path to cover eachpoint in the range [1,m]. In this case x[1...m]=[1,2,3...m] The outputwill be the y-coordinate corresponding to each element of [1,2,3...m]--------------------------------------------------------------------------------------------------- 1: For i = 1; i ≦ m; i ++, do  2: if (x[i] ≦xi[1]) do  3: y[i] = yi[1]; 4: end if  5: if (x[i] ≧xi[Ni]) do  6: y[i] = yi[Ni];  7: end if  8: j= 1;  9: while (j ≦m) 10: if (xi[j] >= x[i]) break; 11: j = j + 1; 12:end while 13: newPathInt[i] = yi[j−1] + (yi[j] − yi[j−1])*(x[i] −xi[j−1])/(xi[j]−xi[j−1]); 14: end for---------------------------------------------------------------------------------------------------

Annex 5 Distance To Diagonal(new_pathInt) //this algorithm approximatesthe warp with a shift. //the shift is the distance between the path andthe diagonal (defined as y=x, or x=i, y=i 1≦i≦m)---------------------------------------------------------------------------------------------------1: Shift=0 2: for i = 1; i ≦ m; i ++, do 3: shift=shift+(new_path(i)−i)4: end for 5: shift=shift/m---------------------------------------------------------------------------------------------------

1. A method of reducing jitter error in a laser scanning system adaptedto produce a scanned image comprising a number of lines of an object,the method comprising the steps of: providing a reference objectarranged such that the scanned image produced by the laser scanningsystem includes a reference image of the reference object; processingthe reference image to calculate an error arising from non-repeatabledisplacement of the lines of the reference image; and adjusting at leastone operating parameter of the laser scanning system in response to thecalculated error.
 2. The method according to claim 1, wherein thereference object is periodic in the direction of the line of scan of thelaser scanning system.
 3. The method according to claim 1, wherein thereference object includes a series of alternate black and white bands.4. The method according to claim 3, wherein the alternate black andwhite bands are equally spaced.
 5. The method according to claim 4,wherein the width of each band is between 0.25 mm and 0.75 mm.
 6. Themethod according to claim 1, wherein the reference image comprises anumber of pixels.
 7. The method according to claim 1, wherein the stepof processing the reference image includes assigning one column of thereference image as the reference column.
 8. The method according toclaim 7, wherein the reference column is located around the centre ofthe reference image.
 9. The method according to claim 1, wherein thestep of processing the reference image includes generating data signalsfor one or more columns which are representative of the imageinformation of the column.
 10. The method according to claim 9, whereinthe image information of the column includes the light intensity, orbrightness, of the image and the data signals include values which arerepresentative of this intensity, or brightness.
 11. The methodaccording to claim 6, wherein the light intensity, or brightness,includes the light intensity or brightness of each pixel in thereference image.
 12. The method according to claim 9, wherein datasignals are generated for each column of the reference image.
 13. Themethod according to claim 12, wherein the step of processing thereference image further includes comparing the reference column datasignal with one or more data signals from the other columns.
 14. Themethod according to claim 13, wherein the reference column data signalis compared with every other column data signal.
 15. The methodaccording to claim 13, wherein the comparison between the referencecolumn data signal and the other column data signals further includesdetermining the similarities between the signals.
 16. The methodaccording to claim 14, wherein the comparison between the referencecolumn data signal and the other column data signals includesdetermining the warping between the signals.
 17. The method according toclaim 16, wherein the comparison between the reference column datasignal and the other column data signals includes using a dynamic timewarping algorithm.
 18. The method according to claim 17, wherein thecomparison between the reference column data signal and the other columndata signals includes using a derivative dynamic time warping algorithm.19. The method according to claim 13, wherein the comparison between thereference column data signal and the other column data signal includesgenerating a matrix which is representative of the pair-wise distancesbetween the reference column data signal and the other column datasignal.
 20. The method according to claim 19, wherein a matrix isgenerated for each comparison of the reference column data signal withevery other column data signal.
 21. The method according to claim 19,wherein the distances between each column are defined in terms of pixelsand the distance between corresponding points of each signal isrepresented by an integer number of pixels.
 22. The method according toclaim 13, wherein the comparison between the reference column datasignal and the other column data signal includes generating a matrixwhich is representative of the pair-wise distances between thederivative of the reference column data signal and the derivative of theother column data signal.
 23. The method according to claim 22, whereina matrix is generated for each comparison of the reference column datasignal with every other column data signal.
 24. The method according toclaim 22, wherein the derivative is the pair-wise distances between thefirst derivative of the reference column data signal and the derivativeof each of the other column data signals.
 25. The method according toclaim 13, wherein the comparison between the reference column datasignal and the other column data signals includes determining a functionrepresentative of the minimal distance path of the matrix.
 26. Themethod according to claim 25, wherein the determination of the functionrepresentative of the minimal distance path of the matrix includesapplying one or more constraints.
 27. The method according to claim 26,wherein the constraints include that the function satisfies a boundarycondition criteria, where the starting and end points of the functionmust be the first and last points of the sequence.
 28. The methodaccording to claim 26, wherein the constraints further include that thefunction satisfies the monotonicity criteria.
 29. The method accordingto claim 26, wherein the constraints further include that the functionsatisfies the continuity criteria.
 30. The method according to claim 1,wherein the step of processing the reference image further includesdetermining an approximate signal shift between the reference columndata signal and each of the other column data signals.
 31. The methodaccording to claim 30, wherein the signal shift corresponds to a columnshift in the reference image.
 32. The method according to claim 31,wherein the column shift corresponds to the error arising from thequasi-periodic displacement of the columns of the reference image. 33.The method according to claim 30, wherein the determination of theapproximate signal shift between the reference column data signal andthe other column data signals includes transforming a parametricrepresentation of the function to an explicit form.
 34. The methodaccording to claim 33, wherein the transformation includes removingduplicates of the abscissas of the parametric curve.
 35. The methodaccording to claim 33, wherein the transformation includes interpolationof the explicit form of the function.
 36. The method according to claim35, wherein the determination of the approximate signal shift betweenthe reference column data signal and each of the other column datasignals includes determining the distance between the interpolated pathdefined by the explicit function and a reference path in the matrix. 37.The method according to claim 36, wherein the reference path in thematrix corresponds to the matrix diagonal.
 38. The method according toclaim 1, wherein the step of processing the reference image includesdetermining an average approximate signal shift for all column datasignals originating from the same portion of the scanning element of thelaser scanning system.
 39. The method according to claim 1, wherein thestep of processing the reference image includes determining an averageapproximate signal shift for all column data signals originating fromthe same facet of the rotating polygonal mirror.
 40. The methodaccording to claim 1, wherein the step of adjusting the at least oneoperating parameter of the laser scanning system in response to thecalculated error may include adjusting the capture time of the first orsecond scanning elements.
 41. The method according to claim 40, whereinthe capture time of the first or second scanning element is advancedand/or delayed.
 42. The method according to claim 40, wherein, when thefirst or second scanning element is a rotating polygonal mirror, eachfacet of the polygon has a specific capture time.
 43. The methodaccording to claim 42, wherein the capture time for each facet of thepolygon is determined by advancing or delaying a reference capture timeby a factor dependent upon the average approximate signal shift for thatspecific portion of the scanning element.
 44. The method according toclaim 1, wherein the laser scanning system further comprises a source ofcollimated light.
 45. The method according to claim 1, wherein the laserscanning system further comprises first and second scanning elements.46. The method according to claim 45, wherein the first scanning elementis a rotating polygonal minor and the second scanning element is anoscillating plane mirror.
 47. The method according to claim 45, whereinthe reference object is positioned in the optical path of the laserscanning system after the first scanning element.
 48. The methodaccording to claim 45, wherein the source of collimated light and thefirst and second scanning elements combine to provide a two-dimensionalcollimated light scan.
 49. The method according to claim 45 any ofclaims 45 to 48, wherein the second scanning element is positioned inthe optical path of the laser scanning system after the first scanningelement and the reference object is positioned after the second scanningelement.
 50. The method according to claim 1, wherein the laser scanningsystem further comprises scan transfer means having two foci.
 51. Themethod according to claim 50, wherein the source of collimated light andthe first and second scanning elements combine to provide atwo-dimensional collimated light scan from an apparent point source, andthe apparent point source is provided at a first focus of the scantransfer means and an object is accommodated at a second focus of thescan transfer means, and wherein the scan transfer means transfers thetwo-dimensional collimated light scan from the apparent point source tothe object.
 52. The method according to claim 51, wherein the object isan eye and the scan transfer means transfers the two-dimensionalcollimated light scan from the apparent point source into the eye. 53.The method according to claim 50, wherein the scan transfer meanscomprises on of the group consisting of an elliptical minor, anasphehcal minor, an ellipsoidal minor, a pair of parabola minors or apair of paraboloidal minors.
 54. The method according to claim 1,wherein the laser scanning system further comprises scan relay means.55. The method according to claim 54, wherein the source of collimatedlight, the first and second scanning elements and the scan relay meanscombine to provide the two-dimensional collimated light scan from theapparent point source.
 56. The method according to claim 54, wherein thescan relay means comprises two foci.
 57. The method according to claim56, wherein one foci of the scan relay means is coincident with one fociof the scan transfer means.
 58. The method according to claim 54,wherein the scan relay means may comprise one of the group consisting ofan elliptical minor, an asphehcal minor, an ellipsoidal minor, a pair ofparabola minors or a pair of paraboloidal minors.
 59. The methodaccording to claim 54, wherein the reference object is located on one ofthe scan transfer means or scan relay means.
 60. The method according toclaim 1, wherein the scanned image produced by the laser scanning systemincludes an image of the object and the reference image of the referenceobject.
 61. The method according to claim 60, wherein the image of theobject and the reference image of the reference object occur beside oneanother on the scanned image.
 62. A minor for a laser scanning systemincluding a reference object.
 63. The mirror according to claim 62,wherein the reference object is periodic in the direction of the line ofscan of the laser scanning system.
 64. The mirror according to claim 63,wherein the reference object is made up of a series of alternate blackand white bands.
 65. The minor according to claim 62, wherein the mirrormay be an elliptical mirror, an aspherical mirror, an ellipsoidal minor,a parabola minor or a paraboloidal mirror.